In the context of probability, what does it mean to say that the trials of an experiment are independent?

• A. Each trial must have the same probability of success as the previous trial.
• B. The sum of the probabilities of all possible outcomes in each trial is less than $1$.
• C. The outcome of any one trial does not affect the outcome of any other trial.
• D. The trials are performed at the same time.

Answer: (C)

Verified step by step guidance

1. Understand that in probability, independence of trials means that the result of one trial does not influence the result of another trial.
2. Recognize that independence implies the probability of an event occurring in one trial remains unchanged regardless of the outcomes of previous trials.
3. Note that this concept is different from having the same probability of success in each trial, which refers to identical distribution but not necessarily independence.
4. Recall that the sum of probabilities of all possible outcomes in a trial must equal 1, not less than 1, so that option is incorrect.
5. Conclude that the correct interpretation of independent trials is: 'The outcome of any one trial does not affect the outcome of any other trial.'